Challenge: Subspace Dimension Finder

Statement

Write a smallestSubspaceDimensionFinder function that accepts a collection of four vectors in the $\R^{5}$, say, $S = \{v_1, v_2, v_3 , v_{4}\}$. The function should find and return the dimensions of the smallest subspace that contains these four vectors.

Sample inputs and outputs

The following table provides sample inputs and corresponding outputs.

Input	Output
$[[5,3,2,3,7],[6,7,2,1,8],[5,3,2,3,7],$$[11,10,4,4,15]]$	2
$[[7,50,5,4,1],[9,7,3,1,5],[6,9,1,50,7],$$[34,52,13,83,12]]$	4

Try it yourself

The signature of the function is given below: